best non interstate route from Cottonwood to Albuquerque

Don't know if you've already headed out, but I'd take US 89A through Oak Canyon to Flagstaff then east on I-40. Walnut Canyon NM is an interesting stop if you can deal with the hiking. East from there you'll hit Petrified Forest NM. However you want to route it, I'd recommend NM %# to take you past El Morro NM and El Malpais NM. We been to quite a few NP's and NM's and El Moro was really quite an interesting, worthwhile stop. You can do it in a couple of hours.